Why cannot we have a strongly consistent family of skew normal (And higher order) distributions

© Springer International Publishing AG 2017. In many practical situations, the only information that we have about the probability distribution is its first few moments. Since many statistical techniques requires us to select a single distribution, it is therefore desirable to select, out of all pos...

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Main Authors: Thongchai Dumrongpokaphan, Vladik Kreinovich
Format: Book Series
Published: 2018
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Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85012925157&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/57128
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spelling th-cmuir.6653943832-571282018-09-05T03:35:18Z Why cannot we have a strongly consistent family of skew normal (And higher order) distributions Thongchai Dumrongpokaphan Vladik Kreinovich Computer Science © Springer International Publishing AG 2017. In many practical situations, the only information that we have about the probability distribution is its first few moments. Since many statistical techniques requires us to select a single distribution, it is therefore desirable to select, out of all possible distributions with these moments, a single “most representative” one. When we know the first two moments, a natural idea is to select a normal distribution. This selection is strongly consistent in the sense that if a random variable is a sum of several independent ones, then selecting normal distribution for all of the terms in the sum leads to a similar normal distribution for the sum. In situations when we know three moments, there is also a widely used selection—of the so-called skew-normal distribution. However, this selection is not strongly consistent in the above sense. In this paper, we show that this absence of strong consistency is not a fault of a specific selection but a general feature of the problem: for third and higher order moments, no strongly consistent selection is possible. 2018-09-05T03:35:18Z 2018-09-05T03:35:18Z 2017-02-01 Book Series 1860949X 2-s2.0-85012925157 10.1007/978-3-319-50742-2_4 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85012925157&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/57128
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Computer Science
spellingShingle Computer Science
Thongchai Dumrongpokaphan
Vladik Kreinovich
Why cannot we have a strongly consistent family of skew normal (And higher order) distributions
description © Springer International Publishing AG 2017. In many practical situations, the only information that we have about the probability distribution is its first few moments. Since many statistical techniques requires us to select a single distribution, it is therefore desirable to select, out of all possible distributions with these moments, a single “most representative” one. When we know the first two moments, a natural idea is to select a normal distribution. This selection is strongly consistent in the sense that if a random variable is a sum of several independent ones, then selecting normal distribution for all of the terms in the sum leads to a similar normal distribution for the sum. In situations when we know three moments, there is also a widely used selection—of the so-called skew-normal distribution. However, this selection is not strongly consistent in the above sense. In this paper, we show that this absence of strong consistency is not a fault of a specific selection but a general feature of the problem: for third and higher order moments, no strongly consistent selection is possible.
format Book Series
author Thongchai Dumrongpokaphan
Vladik Kreinovich
author_facet Thongchai Dumrongpokaphan
Vladik Kreinovich
author_sort Thongchai Dumrongpokaphan
title Why cannot we have a strongly consistent family of skew normal (And higher order) distributions
title_short Why cannot we have a strongly consistent family of skew normal (And higher order) distributions
title_full Why cannot we have a strongly consistent family of skew normal (And higher order) distributions
title_fullStr Why cannot we have a strongly consistent family of skew normal (And higher order) distributions
title_full_unstemmed Why cannot we have a strongly consistent family of skew normal (And higher order) distributions
title_sort why cannot we have a strongly consistent family of skew normal (and higher order) distributions
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85012925157&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/57128
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